# Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning

We consider the estimation of an i.i.d.\ vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise (possibly nonlinear) measurement channel. We present a method, called adaptive generalized approximate message passing (Adaptive GAMP), that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector $\xbf$... (read more)

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